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en:confusions [2019/04/14 23:44] (current)David Zelený[Using the first unconstrained axis in constrained ordination to see how much variation can be maximally explained by a single explanatory variable]

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Problem: You want to know how much variation you can maximally explain by a single explanatory variable in constrained ordination (RDA, tb-RDA, CCA), and for this, you will check the variation represented by the first unconstrained ordination axis of this constrained ordination (with the environmental variable used as explanatory).

Problem: You want to know how much variation you can maximally explain by a single explanatory variable in constrained ordination (RDA, tb-RDA, CCA), and for this, you will check the variation represented by the first unconstrained ordination axis of this constrained ordination (with the environmental variable used as explanatory).

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Explanation:​ If you want to know how much variation you can maximally explain by a single explanatory variable, you follow this logic: the ordination axis of unconstrained ordination (e.g. PCA1) represents the direction of the strongest compositional gradient, and can be (theoretically) considered as a perfect explanatory variable for the dataset from which it was calculated. You can use it as explanatory in the constrained variant of the same ordination method (e.g. RDA) to see how much variation it explains; the same value you get if you simply check the variation represented by this axis in the original unconstrained ordination (the eigenvalue of the axis divided by total inertia/​variance,​ <imgref tbrda-tbpca>,​ the horizontal axis in the left panel). This, however, does not apply to the first unconstrained ordination axis of the constrained ordination (e.g. the PC1 in RDA, <imgref tbrda-tbpca>,​ the vertical axis in the right panel), in which some environmental variable (or variables) was used as explanatory. Such axis represents the maximum variance a single explanatory variable can explain in the dataset after the variation of the explanatory variable has been removed. ​

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Explanation:​ If you want to know how much variation you can maximally explain by a single explanatory variable, you follow this logic: the ordination axis of unconstrained ordination (e.g. PCA1) represents the direction of the strongest compositional gradient, and can be (theoretically) considered as a perfect explanatory variable for the dataset from which it was calculated. You can use it as explanatory in the constrained variant of the same ordination method (e.g. RDA) to see how much variation it explains; the same value you get if you simply check the variation represented by this axis in the original unconstrained ordination (the eigenvalue of the axis divided by total inertia/​variance,​ <imgref tbrda-tbpca>,​ the horizontal axis in the right panel). This, however, does not apply to the first unconstrained ordination axis of the constrained ordination (e.g. the PC1 in RDA, <imgref tbrda-tbpca>,​ the vertical axis in the left panel), in which some environmental variable (or variables) was used as explanatory. Such axis represents the maximum variance a single explanatory variable can explain in the dataset after the variation of the explanatory variable has been removed. ​